stats question

1. Consider the 2-way ANOVA layout yijk = u + ai + Bj + bij + Eijk Eijk ~N (0, 62 ) where factor A has 3 levels (1=3) and factor B has 2 levels (J=2). For simplicity, let's assume that we have a balanced design with K=3. Find the MLE's of the a;'s, | Bj's, Sij's and u. [Hints: To find the MLE, use the usual 4 steps of: (i) writing the likelihood, (ii) calculating the log likelihood, (iii) finding the derivatives with respect to each parameter and (iv) setting the derivatives equal to 0. When writing down the likelihood, remember that observations are independent. Additionally, remember that the ai's, Bj's, Sij's all satisfy constraints. For an example on how to find the MLE's of parameters when there are constraints on the parameters, refer to the example of a multinomial likelihood with probabilities that need to sum up to 1.]